Search

The data behavior of the pion-photon transition form factor (TFF) is discussed using a nonlinear mathematical model with two parameters $B$ and $C$. We show for the Belle data that the inherent inhibition of this model inevitably yields asymptotically to the saturation of the transition form factor in agreement with perturbative QCD. We find that the half-saturated TFF and the asymptotic limit of this model are interrelated and use this property in conjunction with the $1\sigma$ $(B,C)$ confidence ellipse to improve the quality of the fit of the Belle data. We show that the observed asymptotic saturation of the model is analogous to a mechanical system driven by a feedback-loop mechanism. The study of another parametrization without inhibition reveals that in this case asymptotic stability is not possible so that the uninhibited TFF continues to grow. In order to compare the key features of these two fit models, a conformity protocol in terms of QCD-based criteria is proposed., Comment: 7 pages, 5 figures 2 column format

We study two versions of lightcone sum rules to calculate the $\gamma^*\gamma\rightarrow\pi^0$ transition form factor (TFF) within QCD. While the standard version is based on fixed-order perturbation theory by means of a power-series expansion in the strong coupling, the new method incorporates radiative corrections by renormalization-group summation and generates an expansion within a generalized fractional analytic perturbation theory involving only analytic couplings. Using this scheme, we determine the relative nonperturbative parameters and the first two Gegenbauer coefficients of the pion distribution amplitude (DA) to obtain TFF predictions in good agreement with the preliminary BESIII data, while the best-fit pion DA satisfies the most recent lattice constraints on the second moment of the pion DA at the three-loop level., Comment: 8 pages, 3 figures. Work dedicated to the memory of Maxim Polyakov, a deeply admired colleague and friend of ours. Presented at Virtual Tribute to Quark Confinement and the Hadron Spectrum, August 2nd-6th, 2021

We discuss cross-link relations between the $\pi$ and $\rho$-meson channels emerging from two different descriptions of the QCD vacuum: Instanton physics and QCD sum rules with nonlocal condensates (NLC). We derive in both schemes an intriguing linear relation between the $\pi$ and the $\rho^\|$-meson distribution amplitudes in terms of their conformal coefficients and work out the specific impact of the scalar NLC in these two channels. Using a simple model with Gaussian decay of the scalar NLC, we are able to relate it to the moments of the pion non-singlet parton distribution function measurable in experiment -- a highly nontrivial result. The implications for the pion and the $\rho^\|$-meson DAs entailed by the obtained cross-link relations are outlined in terms of two generic scenarios., Comment: 9 pages, 1 table, 4 figures. V2 matches published version

We show that using renormalization-group summation to generate the QCD radiative corrections to the $\pi-\gamma$ transition form factor, calculated with lightcone sum rules (LCSR), renders the strong coupling free of Landau singularities while preserving the QCD form-factor asymptotics. This enables a reliable applicability of the LCSR method to momenta well below 1 GeV$^2$. This way, one can use the new preliminary BESIII data with unprecedented accuracy below 1.5 GeV$^2$ to fine tune the prefactor of the twist-six contribution. Using a combined fit to all available data below 3.1 GeV$^2$, we are able to determine all nonperturbative scale parameters and a few Gegenbauer coefficients entering the calculation of the form factor. Employing these ingredients, we determine a pion distribution amplitude with conformal coefficients $(b_2,b_4)$ that agree at the $1\sigma$ level with the data for $Q^2 \leqslant 3.1$ GeV$^2$ and fulfill at the same time the lattice constraints on $b_2$ at N$^3$LO together with the constraints from QCD sum rules with nonlocal condensates.The form-factor prediction calculated herewith reproduces the data below 1 GeV$^2$ significantly better than analogous predictions based on a fixed-order power-series expansion in the strong coupling constant., Comment: 15 pages, 3 figures, 1 table, [v3] reformatted in two-column style, 15 pages; references added, typos corrected, [v4] minor corrections

We study the pion-photon transition form factor (TFF) $F^{\gamma*\gamma\pi^0}(Q^2)$ using a state-of-the art implementation of light cone sum rules (LCSRs) within fixed-order QCD perturbation theory. The spectral density in the dispersion relation includes all currently known radiative corrections up to the next-to-next-to-leading-order (NNLO) and all twist contributions up to order six. Predictions for the TFF are obtained for various pion distribution amplitudes (DAs) of twist two, including two-loop evolution which accounts for heavy-quark mass thresholds. The influence of the main theoretical uncertainties is quantified in order to enable a more realistic comparison with the data. The characteristics of various pion DAs are analyzed in terms of the conformal coefficients $a_2$ and $a_4$ in comparison with the $1\sigma$ and $2\sigma$ error regions of the data and the most recent lattice constraints on $a_2$ with NLO and NNLO accuracy. Our results provide more stringent bounds on the variation of the pion DA and illuminate the corresponding asymptotic behavior of the calculated TFF., Comment: 16 pages, 3 tables, 4 figures; derives partly from arXiv:1904.02631; text revised and expanded; more and updated figures; references added; discussion of new results. References added. V3 matches version accepted for publication in Physical Review D

We consider the lightcone sum-rule (LCSR) description of the pion-photon transition form factor in combination with the renormalization group of QCD. The emerging scheme represents a certain version of Fractional Analytic Perturbation Theory and significantly extends the applicability domain of perturbation theory towards lower momenta $Q^2\lesssim 1$ GeV$^2$. We show that the predictions calculated herewith agree very well with the released preliminary data of the BESIII experiment, which have very small errors just in this region, while the agreement with other data at higher $Q^2$ is compatible with the LCSR predictions obtained recently by one of us using fixed-order perturbation theory., Comment: 8 pages, 1 figure, talk presented at the "XXIV International Workshop on High Energy Physics and Quantum Field Theory" (22 - 29 September 2019, Sochi, Russia). A number of misprints are corrected

We discuss the evaluation of the transition form factor (TFF) $F^{\gamma*\gamma\pi^0}(Q^2)$ by means of QCD theory and by state-space reconstruction from topological data analysis. We first calculate this quantity in terms of quark-gluon interactions using light cone sum rules (LCSRs). The spectral density includes radiative corrections in leading, next-to-leading, and next-to-next-to-leading-order of perturbative QCD. Besides, it takes into account the twist-four and twist-six terms. The hard-scattering part in the LCSR is convoluted with various pion distribution amplitudes with different morphologies in order to obtain a wide range of predictions for the form factor, including two-loop evolution which accounts for heavy-quark thresholds. We then use nonlinear time series analysis to extract information on the long-term $Q^2$ behavior of the measured scaled form factor in terms of state-space attractors embedded in $\mathbb{R}^3$. These are reconstructed by applying the Packard-Takens method of delays to appropriate samplings of the data obtained in the CLEO, \textit{BABAR}, and Belle single-tagged $e^+e^- \to e^+e^-\pi^0$ experiments. The corresponding lag plots show an aggregation of states around the value $Q^2F^{\gamma*\gamma\pi^0}(Q^2) \approx 0.165\pm 0.005$ GeV pertaining to the momentum interval $Q^2\in [9-11]$~GeV$^2$. We argue that this attractor portrait is a transient precursor of a distribution of states peaking closer to the asymptotic limit $Q^2F^{\gamma*\gamma\pi^0}(Q^2\to \infty)=\sqrt{2}f_\pi$~GeV. More data with a regular increment of 1~GeV$^2$ in the range between 10 and 25~GeV$^2$ would be sufficient to faithfully determine the terminal portrait of the attractor., Comment: 26 pages, 2 tables, 9 figures, uses two-column format. In V2, url's in [22] and [24] removed to resolve problem with format. V3 contains in Figs. 2, 3, 8, 9 comparison with preliminary BESIII data [48] and extended explanations in text

We consider the lightcone sum-rule description of the pion-photon transition form factor, based on dispersion relations, in combination with the renormalization group of QCD, in terms of the formal solution of the Efremov-Radyushkin-Brodsky-Lepage evolution equation, and show that the emerging scheme amounts to a certain version of Fractional Analytic Perturbation Theory (FAPT). In order to ensure the correct asymptotic behavior of the considered physical quantity, this modified FAPT version has to be supplemented by process-specific boundary conditions---in contrast to the standard one. However, it provides the advantage of significantly improving the inclusion of radiative corrections in the low-momentum regime of QCD perturbation theory using renormalization-group summation., Comment: 21 pages, 7 figures. This version implements the Erratum published in Phys. Rev. D 101,059901(E)(2020). The figures have been updated accordingly

A survey is presented on the current status of 3D nucleon tomography. Several research frontiers are addressed that dominate modern physics from theory to current and future experiments. We have now a much more detailed spatial image of the nucleon thanks to various theoretical concepts and methods to describe its charge distribution and spin decomposition which are highlighted here. The progress of lattice computations of these quantities is reported and the prospects of what we can come to expect in the near future are discussed. Multi-dimensional maps of the nucleon's partonic structure appear now within reach of forthcoming experiments., Comment: Based on the Plenary Round Table at XII Quark Confinement and the Hadron Spectrum, 29 August - 3 September, 2016, Thessaloniki, Greece, 32 pages, 1 Table 17 Figures (embedded as pdf). arXiv admin note: text overlap with arXiv:1208.1244

We consider the pion-photon transition form factor at low to intermediate spacelike momenta within the theoretical framework of light-cone sum rules. We derive predictions which take into account all currently known contributions stemming from QCD perturbation theory up to the next-to-next-to-leading order (NNLO) and by including all twist terms up to order six. In order to enable a more detailed comparison with forthcoming high-precision data, we also estimate the main systematic theoretical uncertainties, stemming from various sources, and discuss their influence on the calculations --- in particular the dominant one related to the still uncalculated part of the NNLO contribution. The analysis addresses, in broad terms, also the role of the twist-two pion distribution amplitude derived with different approaches., Comment: 10 pages, 3 figures, Based on the talk given at the XIIth International Conference "Quark Confinement and the Hadronic Spectrum" (Thessaloniki, Greece, 28 August - 4 September 2016)

We consider the calculation of the pion-photon transition form factor $F^{\gamma^*\gamma\pi^0}(Q^2)$ within light-cone sum rules focusing attention to the low-mid region of momenta. The central aim is to estimate the theoretical uncertainties which originate from a wide variety of sources related to (i) the relevance of next-to-next-to-leading order radiative corrections (ii) the influence of the twist-four and the twist-six term (iii) the sensitivity of the results on auxiliary parameters, like the Borel scale $M^2$, (iv) the role of the phenomenological description of resonances, and (v) the significance of a small but finite virtuality of the quasireal photon. Predictions for $F^{\gamma^*\gamma\pi^0}(Q^2)$ are presented which include all these uncertainties and found to comply within the margin of experimental error with the existing data in the $Q^2$ range between 1 and 5 GeV$^2$, thus justifying the reliability of the applied calculational scheme. This provides a solid basis for confronting theoretical predictions with forthcoming data bearing small statistical errors., Comment: 15 pages, 4 figures. Version 3 includes complete Fig. 4 and all Eqs.(B7). Conclusions unchanged; matches version to appear in Phys. Rev. D

We attempt to identify a path layout in the definition of transverse-momentum-dependent T-odd parton distribution functions (TMD)s which combines features of both, initial- and final-state interactions, so that it remains universal despite the fact that the Wilson lines entering such TMDs change their orientation. The generic structure of the quark correlator for this path layout is calculated., Comment: Proceedings for Light Cone 2015, 5 pages. Current version accepted for publication in Few-Body Systems

The pion-photon transition form factor is studied by employing two types of Sum Rules: Light Cone Sum Rules (LCSR) and Anomaly Sum Rules (ASR). By comparing the predictions for the pion-photon transition form factor, obtained from these two approaches, the applicability limit of the LCSRs at low momenta is determined. Reciprocally, the ASR threshold dependence on the momentum was extracted using our LCSR-based method in combination with two different types of pion distribution amplitudes and found that at higher Q2 it approaches a constant., Comment: LaTeX, 16 pages, 2 figures

Using QCD sum rules with nonlocal condensates, we show that the distribution amplitude of the longitudinally polarized $\rho$-meson may have a shorttailed platykurtic profile in close analogy to our recently proposed platykurtic distribution amplitude for the pion. Such a chimera distribution de facto amalgamates the broad unimodal profile of the distribution amplitude, obtained with a Dyson-Schwinger equations-based computational scheme, with the suppressed tails characterizing the bimodal distribution amplitudes derived from QCD sum rules with nonlocal condensates. We argue that pattern formation, emerging from the collective synchronization of coupled oscillators, can provide a single theoretical scaffolding to study unimodal and bimodal distribution amplitudes of light mesons without recourse to particular computational schemes and the reasons for them., Comment: 13 pages, 4 figures. In v2 a typo in Eq. (12) corrected. V3 contains clarifications in text; typos corrected; Table expanded; new references included and discussed; conclusions unchanged; matches version to be published in Nucl. Phys. A. V4: typos in AdS/QCD entries in Table I and in text, bottom of page 5, corrected. In v6 typo in expression for gauge link below Eq. (1) corrected

We provide an in-depth analysis of the $\pi$ distribution amplitude in terms of two different Gegenbauer representations. Detailed predictions for the $\pi-\gamma$ transition form factor are presented, obtained with light-cone sum rules. Various $\pi$ distribution amplitudes are tested and the crucial role of their endpoint behavior in the form-factor analysis is discussed. Comparison with the data is given., Comment: 7 pages, 3 figures. Based on talk by first author at LIGHTCONE 2014, May 26-30, 2014, Raleigh, NC, USA. Accepted for publication in Few-Body Systems

The binding effects of quarks within hadrons are discussed in terms of the pion distribution amplitude over longitudinal momentum fractions. To understand the behavior of this quantity at different momentum scales, the concept of synchronization in complex systems has been employed. It is argued that at low momentum scales, the quarks get correlated by nonlocal quark/gluon condensates that cause an endpoint-suppressed, mainly bimodal structure of the pion distribution amplitude inferred from a sum-rule analysis. The mass generation mechanism, within the framework of Dyson-Schwinger equations, and evolution effects pull these two peaks back to the center to form at $Q^2\to\infty$ the asymptotic distribution amplitude which represents the most synchronized $\bar{q}q$ state., Comment: 5 pages, 3 figures embedded; v2 includes remarks on and references to AdS/QCD; v3 has 6 pages, new material on short-tailed platykurtic distribution amplitude and minor corrections and clarifications added; abstract extended and references updated

We highlight the progress, current status, and open challenges of QCD-driven physics, in theory and in experiment. We discuss how the strong interaction is intimately connected to a broad sweep of physical problems, in settings ranging from astrophysics and cosmology to strongly-coupled, complex systems in particle and condensed-matter physics, as well as to searches for physics beyond the Standard Model. We also discuss how success in describing the strong interaction impacts other fields, and, in turn, how such subjects can impact studies of the strong interaction. In the course of the work we offer a perspective on the many research streams which flow into and out of QCD, as well as a vision for future developments., Comment: 246 pp, around 128 figures; v2 adds material, references, and corrections suggested by readers of v1 -- to be submitted to EPJC

Detailed predictions for the scaled pion-photon transition form factor are given, derived with the method of light-cone sum rules and using pion distribution amplitudes with two and three Gegenbauer coefficients obtained from QCD sum rules with nonlocal condensates. These predictions agree well with all experimental data that are compatible with QCD scaling (and collinear factorization), but disagree with the high-$Q^2$ data of the BaBar Collaboration that grow with the momentum. A good agreement of our predictions with results obtained from AdS/QCD models and Dyson-Schwinger computations is found., Comment: 10 pages, 4 figures, 6 references added, minor style corrections, Presented by the first author at the Light-Cone Conference 2013, May 20-24, 2013, Skiathos, Greece

We show that the geometry of the Wilson lines, entering the operator definition of the transverse-momentum dependent parton distributions and that of the soft factor, follows from the kinematics of the underlying physical process in conjunction with the gauge invariance of the QCD Lagrangian. We demonstrate our method in terms of concrete examples and determine the paths of the associated Wilson lines. The validation of the factorization theorem in our approach is postponed to future work., Comment: 10 pages, 2 figures. Invited contribution presented by the first author at the Lightcone 2013+ Conference, Skiathos, Greece, 20-24 May, 2013. Matches version to appear in Few Body Systems

The leading-twist distribution amplitude for the longitudinal rho-meson was studied using QCD Sum Rules with nonlocal condensates and a spectral density which includes next-to-leading order radiative corrections. The obtained profile is compared with results from standard QCD sum rules, lattice QCD, holographic QCD, a light-front quark model, and the instanton liquid model. Preliminary estimates for the first two moments of the transverse $\rho$-meson distribute amplitude are also given., Comment: 6 pages, 2 figures, 2 tables, talk presented by the first author at the Light-Cone Conference 2013, May 20-24, 2013, Skiathos, Greece. v2 minor corrections

An outstanding goal of physics is to find solutions that describe hadrons in the theory of strong interactions, Quantum Chromodynamics (QCD). For this goal, the light-front Hamiltonian formulation of QCD (LFQCD) is a complementary approach to the well-established lattice gauge method. LFQCD offers access to the hadrons' nonperturbative quark and gluon amplitudes, which are directly testable in experiments at existing and future facilities. We present an overview of the promises and challenges of LFQCD in the context of unsolved issues in QCD that require broadened and accelerated investigation. We identify specific goals of this approach and address its quantifiable uncertainties., Comment: White Paper of International Light Cone Advisory Committee

The new data on the $\gamma^*\gamma \to \pi^0$ transition form factor of the Belle Collaboration are analyzed in comparison with those of BaBar (including the older data of CELLO and CLEO) using an approach based on light-cone sum rules. Performing a 2-, and a 3-parametric fit to these data, we found that the Belle and the BaBar data have no overlap at the $1\sigma$ level. While the Belle data agree with our predictions, the Babar data are in conflict with them., Comment: 8 pages, 6 figures, Presented at Light-Cone 2012, July 08-13, 2012, Cracow, Poland

This report attempts to capture the essential workings of gauge links (Wilson lines) inside gauge-invariant formulations of parton distribution functions in QCD and gain some deeper insight into their key (renormalization) properties. We show, in particular, that the one-loop anomalous dimension of the Cherednikov-Stefanis quark TMD PDF is in the lightcone gauge $A^+=0$, combined with the Mandelstam--Leibbrandt pole prescription, the same as that obtained in the special covariant gauge $a=-3$, leaving no uncanceled rapidity singularities., Comment: 8 pages, 2 figures. Presented at Light-Cone 2012, July 08-13, 2012, Cracow, Poland. Dedicated to the memory of Walter Gloeckle, teacher, friend, and colleague. V2 has a couple of minor corrections. V3 matches version accepted for publication in Acta Physica Polonica B

We extract constraints on the pion distribution amplitude from available data on the pion-photon transition form factor in the framework of light-cone sum rules. A pronounced discrepancy $(2.7-3)\sigma$ between the Gegenbauer expansion coefficients extracted from the CELLO, CLEO, and Belle experimental data relative to those from BaBar is found. Predictions for the pion-photon transition form factor are presented by employing a pion distribution amplitude obtained long ago from QCD sum rules with nonlocal condensates. These predictions comply with the Belle data but disagree with those of BaBar beyond 9 GeV$^2$., Comment: 5 pages, 3 figures, talk presented by the first author at the QCD@Work Conference, Lecce (Italy), 18 - 21 June, 2012. v2 minor typos corrected

We perform a comparative theoretical study of the data at spacelike momentum transfer for the $\gamma^*\gamma\to\pi^0$ transition form factor, just reported by the Belle Collaboration, vs. those published before by BaBar, also including the older CLEO and CELLO data. Various implications for the structure of the $\pi^0$ distribution amplitude vis-\`a-vis those data are discussed and the existing theoretical predictions are classified into three distinct categories. We argue that the actual bifurcation of the data with antithetic trends is artificial and reason that the Belle data are the better option., Comment: v1: 5 pages, 1 table, 2 figures. v2: 1 figure added and discussed in text; references regrouped, added and/or updated. v3: matches version to be published in PRD

A state-of-the-art analysis of the pion-photon transition form factor is presented based on an improved theoretical calculation that includes the effect of a finite virtuality of the quasi-real photon in the method of light-cone sum rules. We carry out a detailed statistical analysis of the existing experimental data using this method and by employing pion distribution amplitudes with up to three Gegenbauer coefficients $a_2, a_4, a_6$. Allowing for an error range in the coefficient $a_6\approx 0$, the theoretical predictions for $\gamma^*\gamma\to\pi^0$ obtained with nonlocal QCD sum rules are found to be in good agreement with all data that support a scaling behavior of the transition form factor at higher $Q^2$, like those of the Belle Collaboration. The data on $\gamma^*\gamma\to\eta/\eta'$ from CLEO and \babar are also reproduced, while there is a strong conflict with the auxetic trend of the \babar data above 10 GeV$^2$. The broader implications of these findings are discussed., Comment: v4: 13 pages, 1 table, 8 figures. Paper body radically redesigned and extended to include Belle data. Contains statistical data analysis and photon small virtuality. Conclusions and references updated. V5 matches version to appear in Physical Review D

We discuss the possibility of non-minimal gauge invariance of transverse-momentum-dependent parton densities (TMDs) that allows direct access to the spin degrees of freedom of fermion fields entering the operator definition of (quark) TMDs. This is achieved via enhanced Wilson lines that are supplied with the spin-dependent Pauli term $\sim F^{\mu\nu}[\gamma_\mu, \gamma_\nu]$, thus providing an appropriate tool for the "microscopic" investigation of the spin and color structure of TMDs. We show that this generalization leaves the leading-twist TMD properties unchanged but modifies those of twist three by contributing to their anomalous dimensions. We also comment on Collins' recent criticism of our approach., Comment: 4 pages. Presented at the XIV Workshop on High Energy Spin Physics, 20-24 Sept 2011, Dubna, Russia

We present an extended analysis of the data for the pion-photon transition form factor from different experiments, CELLO, CLEO, and BaBar, and discuss various theoretical approaches which try to reason from them. We focus on the divergent behavior of the BaBar data for the pion and those for the $\eta(\eta')$ pseudoscalar mesons and comment on recently proposed explanations for this discrepancy. We argue that it is not possible at present to accommodate these data within the standard QCD framework self-consistently., Comment: 5 pages, 2 figures, talk presented by the second author at the International Workshop on e^+e^- collisions from phi to psi (PHIPSI11), Novosibirsk (Russia), Sept. 19--22, 2011

An analysis of all available data (CELLO, CLEO, \babar) in the range $[1\div 40]$ GeV$^2$ for the pion-photon transition form factor in terms of light-cone sum rules with next-to-leading-order accuracy is discussed, including twist-four contributions and next-to-next-to-leading order and twist-six corrections---the latter two via uncertainties. The antithetic trend between the \babar data for the $\gamma^*\gamma\pi^0$ and those for the $\gamma^*\gamma\eta(\eta')$ transition is pointed out, emphasizing the underlying antagonistic mechanisms: endpoint enhancement for the first and endpoint-suppression for the second---each associated with pseudoscalar meson distribution amplitudes with distinct endpoint characteristics., Comment: 6 pages, 3 figures; needs style files svglov2.clo, svjour2.cls (supplied). Presented at LIGHTCONE 2011, 23 - 27 May, 2011, Dallas, USA. Accepted for publication in Few-Body Systems. In v2 name of second author in [28] corrected. V3 is final version, published online 23. Sep 2011

A generalized idea of gauge invariance, that embodies into the Wilson lines the spin-dependent Pauli term $\sim F^{\mu\nu}[\gamma_\mu, \gamma_\nu]$, is applied to set up a new framework for the operator definition of transverse-momentum-dependent parton densities (TMDs). We show that such a treatment of gauge invariance is justified, since it does not change the leading-twist behavior of the TMDs, albeit it contributes to their twist-three properties, in particular, to their anomalous dimensions. We discuss other consequences of this generalization and its possible applications to lattice simulations of the TMDs., Comment: 5 pages, 2 figures. Invited talk given at the XIX International Workshop on Deep Inelastic Scattering (DIS 2011), 11 - 15 Apr 2011, Thomas Jefferson National Accelerator Facility, Newport News (VA)

A global fit to the data from different collaborations (CELLO, CLEO, BaBar) on the pion-photon transition form factor is carried out using light-cone sum rules. The analysis includes the next-to-leading QCD radiative corrections and the twist-four contributions, while the main next-to-next-to-leading term and the twist-six contribution are taken into account in the form of theoretical uncertainties. We use the information extracted from the data to investigate the pivotal characteristics of the pion distribution amplitude. This is done by dividing the data into two sets: one containing all data up to 9 GeV$^2$, whereas the other incorporates also the high-$Q^2$ tail of the BaBar data. We find that it is not possible to accommodate into the fit these BaBar data points with the same accuracy and conclude that it is difficult to explain these data in the standard scheme of OCD., Comment: 8pages, 6 Figures, 2 Tables. Talk presented by the second and third authors at the 5th joint International HADRON STRUCTURE '11 Conference, Tatranska Strba (Slovak Republic),June 27--July 1, 2011.v2 minor corrections, 3 references are added

This report is based on a ten-week program on "Gluons and the quark sea at high-energies", which took place at the Institute for Nuclear Theory in Seattle in Fall 2010. The principal aim of the program was to develop and sharpen the science case for an Electron-Ion Collider (EIC), a facility that will be able to collide electrons and positrons with polarized protons and with light to heavy nuclei at high energies, offering unprecedented possibilities for in-depth studies of quantum chromodynamics. This report is organized around four major themes: i) the spin and flavor structure of the proton, ii) three-dimensional structure of nucleons and nuclei in momentum and configuration space, iii) QCD matter in nuclei, and iv) Electroweak physics and the search for physics beyond the Standard Model. Beginning with an executive summary, the report contains tables of key measurements, chapter overviews for each of the major scientific themes, and detailed individual contributions on various aspects of the scientific opportunities presented by an EIC., Comment: 547 pages, A report on the joint BNL/INT/Jlab program on the science case for an Electron-Ion Collider, September 13 to November 19, 2010, Institute for Nuclear Theory, Seattle; v2 with minor changes, matches printed version

We present a completely gauge-invariant operator definition of transverse-momentum-dependent parton densities (TMD), supplied with longitudinal lightlike gauge links as well as transverse gauge links at lightcone infinity. Within this framework, we consider the consistent treatment of specific divergences, emerging in the "unsubtracted" TMD beyond the tree approximation, and construct the soft factors to cancel unphysical singularities. We confront this approach with factorization schemes, which make use of covariant gauges with off-the-lightcone gauge links, and discuss their mutual connection., Comment: 10 pages, 2 figures; needs ws-ijmpcs.cls (supplied). Invited talk presented at Workshop "QCD evolution of parton distributions: from collinear to non-collinear case", 8 - 9 Apr 2011, Thomas Jefferson National Accelerator Facility, Newport News (VA), USA

We perform a detailed analysis of all existing data (CELLO, CLEO, BaBar) on the pion-photon transition form factor by means of light-cone sum rules in which we include the NLO QCD radiative corrections and the twist-four contributions. The NNLO radiative correction together with the twist-six contribution are also taken into account in terms of theoretical uncertainties. Keeping only the first two Gegenbauer coefficients $a_2$ and $a_4$, we show that the $1\sigma$ error ellipse of all data up to 9 GeV$^2$ greatly overlaps with the set of pion distribution amplitudes obtained from nonlocal QCD sum rules---within the range of uncertainties due to twist-four. This remains valid also for the projection of the $1\sigma$ error ellipsoid on the $(a_2,a_4)$ plane when including $a_6$. We argue that it is not possible to accommodate the high-$Q^2$ tail of the BaBar data with the same accuracy, despite opposite claims by other authors, and conclude that the BaBar data still pose a challenge to QCD., Comment: 10 pages, 2 Tables, 4 figures. In v2 some explanations and references added. In v3 some clarifications added and references updated; matches version to appear in Phys. Rev. D

We discuss different operator definitions of the transverse-momentum dependent (TMD) parton densities from the point of view of their renormalization-group (RG) properties and UV evolution. We also consider the structure of the gauge links (Wilson lines) in these operator definitions and examine the role of the soft factor in the factorization formula within the TMD approach to semi-inclusive processes., Comment: 4 pages. Invited talk presented at the INT Program "Gluons and the quark sea at high energies: distributions, polarization, tomography", 13 Sep - 19 Nov 2010 Seattle (WA), USA

We propose a consistent treatment of divergences emerging in the computation of transverse-momentum-dependent parton densities in leading $\alpha_s$-order of QCD perturbation theory., Comment: 3 pages, 1 figure. Talk presented at the International Workshop on Diffraction in High-Energy Physics, 10-15 Sept, 2010, Otranto (Lecce), Italy. v2: affiliation and references corrected

We discuss the end-point behavior of the pion distribution amplitude (DA) and calculate its slope using QCD sum rules with nonlocal condensates. This is done in terms of the standard derivative and also with the help of an "integral derivative", recently obtained by us. Our approach favors a value of the slope of the order (or less) of the asymptotic DA and is in clear disagreement with flat-type pion DAs., Comment: 13 pages, 5 figures, 3 tables, invited talk given by the second author at "QUARKS-2010, 16th International Seminar on High Energy Physics", Kolomna, Russia, 6-12 June, 2010. v2 An important reference is added with a corresponding insertion in the text. v3 minor typos corrected

We discuss the possibility of quantum entanglement for pairs of charged particles produced in high-energy $pp$-collisions at the LHC. Using a framework of interacting Wilson lines, we calculate 2-D and 1-D two-particle angular correlation functions in terms of the differences of the pseudorapidities and azimuthal angles of the produced particles. The calculated near-side angular correlation shows a localized maximum around $\Delta\phi \approx 0$, though it is less pronounced compared to the peak observed by the CMS Collaboration. We argue that this soft correlation is universal and insensitive to the specific properties of the matter (quark-gluon plasma, QCD vacuum, etc.) used to describe hadronic states---though such properties can be included to further improve the results., Comment: v1: 4 pages, 1 figure (eps file embedded in text); v2: 9 pages, 6 eps figures, significantly revised and extended, new results on 2-D and 1-D correlations presented, references updated and added; v3: matches the version accepted for publication in Int. J. Mod. Phys. A; v4: minor corrections, matches the final version in Int. J. Mod. Phys. A

We summarize the renormalization-group properties of transverse-momentum dependent (TMD) parton distribution functions (PDF)s arguing that in the light-cone gauge the overlapping ultraviolet and rapidity divergences cannot be solely controlled by (dimensional) regularization, but necessitate their renormalization. In doing so, we show that at the one-loop order this additional divergence entails an anomalous dimension which can be attributed to a cusp in the gauge contour at light-cone infinity. Then, we present a recent analysis of TMD PDFs which incorporates in the gauge links the Pauli term $\sim F^{\mu\nu}[\gamma_\mu,\gamma_\nu]$. This generalized treatment of gauge invariance is shown to be justified, in the sense that it does not modify the behavior of the leading-twist contribution, though it contributes to the anomalous dimension of that of twist-three. An important consequence of the inclusion of the spin-dependent Pauli term is the appearance of a constant phase---the same for the leading twist-two and subleading distribution functions---that ensues from the interaction of the Pauli term in the transverse gauge link with the gauge field accompanying the fermion. Remarkably, this phase has opposite sign for the Drell-Yan process as compared to the semi-inclusive DIS., Comment: 10 pages, 2 figures embedded as eps files. Invited plenary talk presented by the first author at the "Lightcone Conference 2010", June 14-18, 2010, Valencia, Spain. Needs PoS.cls and PoSlogo.ps (included)

We discuss the state-of-the-art of the theory of transverse-momentum dependent parton densities (TMD)s, paying special attention to their renormalization properties, the structure of the gauge links in the operator definition, and the role of the soft factor in the factorization formula within the TMD approach to the semi-inclusive processes. We argue that the use of the lightcone axial gauge offers certain advantages for a consistent definition of TMDs as compared to the off-the-light-cone gauges, or covariant gauges with off-the-lightcone gauge links., Comment: 7 pages, no figures; needs ws-procs9x6.cls (supplied). Talk presented by the first author at Workshop on "Exclusive Reactions at High Momentum Transfer", 18-21 May 2010, Thomas Jefferson National Accelerator Facility (Newport News, VA, USA)

Starting from the QCD sum rules with nonlocal condensates for the pion distribution amplitude, we derive another sum rule for its derivative and its "integral" derivatives---defined in this work. We use this new sum rule to analyze the fine details of the pion distribution amplitude in the endpoint region $x\sim 0$. The results for endpoint-suppressed and flat-top (or flat-like) pion distribution amplitudes are compared with those we obtained with differential sum rules by employing two different models for the distribution of vacuum-quark virtualities. We determine the range of values of the derivatives of the pion distribution amplitude and show that endpoint-suppressed distribution amplitudes lie within this range, while those with endpoint enhancement---flat-type or CZ-like---yield values outside this range., Comment: 20 pages, 10 figures, 1 table, conclusions updated

We discuss the status of the pion distribution amplitude (DA) in connection with QCD sum rules and experimental data on the $\gamma^*\gamma^\to \pi^0$ transition form factor. Contents: (a) Pion DA in generalized QCD Sum Rules (SRs); (b) Light Cone Sum Rules (LCSR) analysis of the CLEO data for the $\gamma^*\gamma\to\pi^{0}$ transition form factor; (c) Recent lattice QCD data for the pion DA; (d) BaBar data---a challenge for QCD?, Comment: 6 pages, 3 figures, talk delivered by the first author at the International Meeting "Excited QCD'', January 31--February 5, 2010, Tatranska Lomnica (Slovakia)

Results on the resummation of non-power-series expansions of the Adler function of a scalar, $D_S$, and a vector, $D_V$, correlator are presented within fractional analytic perturbation theory (FAPT). The first observable can be used to determine the decay width $\Gamma_{H\to b\bar{b}}$ of a scalar Higgs boson to a bottom-antibottom pair, while the second one is relevant for the $e^+e^-$ annihilation cross section. The obtained estimates are compared with those from fixed-order (FOPT) and contour-improved perturbation theory (CIPT), working out the differences. We prove that although FAPT and CIPT are conceptually different, they yield identical results. The convergence properties of these expansions are discussed and predictions are extracted for the resummed series of $R_S$ and $D_V$ using one- and two-loop coupling running, and making use of appropriate generating functions for the coefficients of the perturbative series., Comment: 34 pages, 7 figures, 7 tables. Version 4: Fig. 4 (left panel) corrected; some typos with Kroneccker symbols in Eqs. (D14) and (D18) corrected

We propose a new framework for transverse-momentum dependent parton distribution functions, based on a generalized conception of gauge invariance which includes into the Wilson lines the Pauli term $\sim F^{\mu\nu}[\gamma_\mu, \gamma_\nu]$. We discuss the relevance of this nonminimal term for unintegrated parton distribution functions, pertaining to spinning particles, and analyze its influence on their renormalization-group properties. It is shown that while the Pauli term preserves the probabilistic interpretation of twist-two distributions---unpolarized and polarized---it gives rise to additional pole contributions to those of twist-three. The anomalous dimension induced this way is a matrix, calling for a careful analysis of evolution effects. Moreover, it turns out that the crosstalk between the Pauli term and the longitudinal and the transverse parts of the gauge fields, accompanying the fermions, induces a constant, but process-dependent, phase which is the same for leading and subleading distribution functions. We include Feynman rules for the calculation with gauge links containing the Pauli term and comment on the phenomenological implications of our approach., Comment: 35 pages, 2 Tables, 5 figures (eps files embedded in text); v2 wrong lettering in Fig. 5 corrected; 1 reference added; some califying remarks in text added and typos removed; matches version to appear in Nucl. Phys. B

Different approaches to define transverse-momentum dependent parton distribution functions are considered from the point of view of their renormalization-group properties. The associated one-loop anomalous dimensions of these quantities are presented and compared to each other. We give arguments in favor of the "pure light-like" definition, and the use of the light-cone gauge., Comment: 4 pages. Talk presented by the first author at Workshop on the International Workshop "Transverse Partonic Structure of Hadrons", 21-26 Jun 2009, Erevan, Armenia

We use light-cone QCD sum rules to calculate the pion-photon transition form factor, taking into account radiative corrections up to the next-to-next-to-leading order of perturbation theory. We compare the obtained predictions with all available experimental data from the CELLO, CLEO, and the BaBar Collaborations. We point out that the BaBar data are incompatible with the convolution scheme of QCD, on which our predictions are based, and can possibly be explained only with a violation of the factorization theorem. We pull together recent theoretical results and comment on their significance., Comment: 10 pages, 4 figures, 3 tables. Presented by the first author at Workshop "Recent Advances in Perturbative QCD and Hadronic Physics", 20--25 July 2009, ECT*, Trento (Italy), in Honor of Prof. Anatoly Efremov's 75th Birthday. v2 wrong reference tag removed. v3 Fig. 4 and Ref. [27] corrected

The ultraviolet and rapidity divergences of transverse-momentum dependent parton distribution functions with lightlike and transverse gauge links is studied, also incorporating a soft eikonal factor. We find that in the light-cone gauge with $q^-$-independent pole prescriptions extra divergences appear which amount, at one-loop, to a cusp-like anomalous dimension. We show that such contributions are absent when the Mandelstam-Leibbrandt prescription is used. In the first case, the soft factor cancels the anomalous-dimension defect, while in the second case its ultraviolet-divergent part reduces to unity., Comment: 10 pages, 3 figures; needs ws-mpla-hep.cls (supplied). Talk presented by the first author at Workshop on "Recent Advances in Perturbative QCD and Hadronic Physics", 20--25 July 2009, ECT*, Trento, Italy, in Honor of Prof. Anatoly Efremov's 75th birthday

We discuss the QCD sum-rule approach for the spacelike electromagnetic pion form factor in the $O(\alpha_s)$ approximation. We show that the nonlocality of the condensates is a key point to include nonperturbative contributions to the pion form factor. We compare our results with the Local-Duality predictions and show that the continuum threshold $s_0(Q^2)$ parameter is highly underestimated in the Local-Duality approach at $Q^2\gtrsim 2$ GeV$^2$. Using our fit for this parameter, $s_0^\text{LD}(Q^2)$, and applying the fractional analytic perturbation theory, we estimate with an accuracy of the order of 1% the $O(\alpha_s^2)$ contribution to the pion's form factor., Comment: 10 pages, 3 figures, talk presented by the first author at Workshop "Recent Advances in Perturbative QCD and Hadronic Physics", 20--25 July 2009, ECT*, Trento (Italy), in Honor of Prof. Anatoly Efremov's 75th Birthday Celebration

We present predictions for the pion-photon transition form factor, derived with the help of light-cone sum rules and including the main part of the NNLO radiative corrections. We show that, when the Bakulev-Mikhailov-Stefanis (BMS) pion distribution amplitude is used, the obtained predictions agree well with the CELLO and the CLEO data. We found that no model distribution amplitude can reproduce the observed $Q^2$ growth of the new BaBar data, though the BMS model complies with several BaBar data points., Comment: 5 pages, 2 figures, 3 tables. Presented by the first author at 3rd joint International HADRON STRUCTURE'09 Conference at Tatranska Strba, Slovakia, August 30th - September 3rd, 2009. v2 Eqs. (9), (10) corrected; wrong reference tag removed. v3 Fig. 2 and Ref. [13] corrected

We review a nonlocal-condensate approach and its application in QCD sum rules for the spacelike electromagnetic pion form factor. It is shown that the nonlocality of the condensates is a key point to include nonperturbative contributions to the pion form factor., Comment: 4 pages, 1 figures, invited talk at the 3rd Joint International Hadron Structure'09 Conference, Tatranska Strba (Slovak Republic), Aug. 30--Sept. 3, 2009